code: def train(
      network_def,
      online_params,
      target_params,
      optimizer,
      optimizer_state,
      states,
      actions,
      next_states,
      rewards,
      terminals,
      loss_weights,
      support,
      cumulative_gamma,
      double_dqn,
      distributional,
      mse_loss,
      rng,
  ):
      """Run a training step."""
  
      # Split the current rng into 2 for updating the rng after this call
      rng, rng1, rng2 = jax.random.split(rng, num=3)
  
      def q_online(state, key):
          return network_def.apply(
              online_params, state, key=key, support=support
          )
  
      def q_target(state, key):
          return network_def.apply(
              target_params, state, key=key, support=support
          )
  
      def loss_fn(params, target, loss_multipliers):
          """Computes the distributional loss for C51 or huber loss for DQN."""
  
          def q_online(state, key):
              return network_def.apply(
                  params, state, key=key, support=support
              )
  
          if distributional:
              logits = get_logits(q_online, states, rng)
              logits = jnp.squeeze(logits)
              # Fetch the logits for its selected action. We use vmap to perform this
              # indexing across the batch.
              chosen_action_logits = jax.vmap(lambda x, y: x[y])(
                  logits, actions
              )
              loss = jax.vmap(
                  losses.softmax_cross_entropy_loss_with_logits
              )(target, chosen_action_logits)
          else:
              q_values = get_q_values(q_online, states, rng)
              q_values = jnp.squeeze(q_values)
              replay_chosen_q = jax.vmap(lambda x, y: x[y])(
                  q_values, actions
              )
  
              loss = losses.mse_loss if mse_loss else losses.huber_loss
              loss = jax.vmap(loss)(target, replay_chosen_q)
  
          mean_loss = jnp.mean(loss_multipliers * loss)
          return mean_loss, loss
  
      # Use the weighted mean loss for gradient computation.
      grad_fn = jax.value_and_grad(loss_fn, has_aux=True)
      target = target_output(
          q_online,
          q_target,
          next_states,
          rewards,
          terminals,
          support,
          cumulative_gamma,
          double_dqn,
          distributional,
          rng1,
      )
  
      # Get the unweighted loss without taking its mean for updating priorities.
      (mean_loss, loss), grad = grad_fn(
          online_params, target, loss_weights
      )
      updates, optimizer_state = optimizer.update(
          grad, optimizer_state, params=online_params
      )
      online_params = optax.apply_updates(online_params, updates)
      return optimizer_state, online_params, loss, mean_loss, rng2
  
imports: import functools
  from absl import logging
  from dopamine.jax import losses
  from dopamine.jax import networks
  from dopamine.jax.agents.dqn import dqn_agent
  from dopamine.jax.agents.rainbow import rainbow_agent
  from dopamine.metrics import statistics_instance
  from dopamine.replay_memory import prioritized_replay_buffer
  import gin
  import jax
  import jax.numpy
  import numpy
  import optax
  import tensorflow
label_desc: Use image node_id 5 for calling a global function with example usage: train(network_def, online_params, target_params, optimizer, optimizer_state, states, actions, next_states, rewards, terminals, loss_weights, support, cumulative_gamma, double_dqn, distributional, mse_loss, rng) and returns: optimizer_state,  online_params,  loss,  mean_loss,  rng2, network_def, network_def, mean_loss,  loss, network_def